The term “group centered” is used in Australia and New Zealand psychodrama circles with respect to warm-up and also with respect to the drama itself.
Firstly with respect to the drama. I recall Max Clayton’s teaching when the group was under the misapprehension that sociodrama was always group centred i.e. without a specific protagonist, and psychodrama always had a protagonist. He then demonstrated a protagonist centred sociodrama, i.e. one based around the social roles in one person’s work situation. On rare occasions, I have seen a group centered psychodrama, one that began as a sociogram. An isolate emerged and the group then worked collaboratively with that person to include them.
With respect to warm-up, I am familiar with the usage where a “director directed warm-up” is contrasted with a “group centered warm-up”.
I have found a passage in “Who Shall Survive?” where Moreno talks about “centeredness.” and his usage is a bit different.
I doubt that we would use “leader centered” for psychodrama. If there is a psychodrama, then it is based on the group or the protagonist as the central focus. Emergent psychodrama sounds interesting but is not related to this discussion as far as I can see. I imagine all our groups are “group centered” in the way the word is used in the passage from “Who Shall Survive?” Even director directed warm-ups lead to group or protagonist centered psychodrama.
What has sparked my interest in this linguistic exploration is that I have been working with couples in groups in a variety of ways. I want to use the words “relationship centered psychodrama”. I think there are many ways to be “relationship centered”. I think more exploration is needed as being protagonist centered can run counter to the needs of a couple. I am writing another post on relationship centered psychodrama as I research the variety of ways this can be done and also the way Moreno tackled this in the past.